Adonalsium

Adonalsium is a mysterious term used in the cosmere, which could refer to the power of Creation or a god. It has not been revealed what Adonalsium explicitly is, but its power is seen in the Shards of Adonalsium, which act as imperfect gods in the cosmere. In The Way of Kings[1] it is implied that there are sixteen Shards.

It has been confirmed that Hoid was present when Adonalsium Shattered[2], that the Shattering left exactly the sixteen Shards it did for a specific reason[3][4], and that the shattering was intentional.[5]

The Shattering may or may not be a result of the failed plot to destroy Adonalsium.[6] At the time of the Shattering, Adonalsium was consciously opposed by something, and that thing is still around.[7] It created some form of weapon.[8]

After Adonalsium shattered into its present form, the pieces were given to or taken by individuals that then had the powers of the aspect of the Shard of Adonalsium. These people tend to act like imperfect gods, capable of creating and destroying worlds. Many of these "gods" give specific magical powers to the people on their worlds, and most of Brandon Sanderson's novels take place in one of these planets. The nature of the common people's powers is modeled after the power of the Shard in question.

The existence of a single origin of these shards have been hinted at in Sanderson's novels:

Ati was the name of the person who held Ruin before being killed by Vin holding Preservation at the end of The Hero of Ages.
Intentionally killing Ati went against the intent of Preservation, but as Vin had not yet become attuned to it, she was able to use its power to her own ends.

It is also possible that those who take the power of a Shard may be able to resist this change to their personality by force of will, like when Sazed gained the powers of both Ruin and Preservation:

“[Ruin and Preservation] threatened to annihilate each other.

And yet, because he was of one mind on how to use them, he could keep them separate.